Some illustrative examples on the analysis of the SW-CRT
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Transcript of Some illustrative examples on the analysis of the SW-CRT
12/05/2015
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Some illustrative examples on the analysis of the SW-CRT
12/05/2015
Karla Hemming
Calendar time is a confounder
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Why calendar time is a confounder…
Time effects
• When designing a SW-CRT time needs to be allowed for in the sample size calculation.
• Time also needs to be allowed for in the analysis
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Analysis
Analysis • Summarise key characteristics by exposure / unexposed status
– Identify selection biases
• Analysis either GEE or mixed models– Clustering– Time effects
• Imbalance of calendar time between exposed / unexposed:– The majority of the control observations will be before the
majority of the intervention observations– Time is a confounder!
• Unadjusted effect meaningless
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Treatment effect
• After accounting for any secular changes, what is the effect of the intervention, averaged across steps?
• The intervention effect is modelled as a change in level, constant across steps (or time)
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Interpretation of intervention effect in SW design: continuous time
Control Intervention
Estimated after averaging across all sites / time points in each condition
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Interpretation of intervention effect in SW: categorical time
Control
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Example one
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Example 1: Maternity sweeping
• Objective: evaluate a training scheme to improve the rate of membrane sweeping in post term pregnancies
– Primary outcome:• Proportion of women having a membrane sweep• Baseline rate 40%• Hope to increase to 50% during 12 weeks post intervention
– Cluster design:• 10 teams (clusters); 12 births per cluster per week• Pragmatic design – rolled out when possible• Transition period to allow training
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Example 1: Maternity sweeping (transition period)
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Example 1: Underlying trend
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Example 1: results Unexposed
to intervention
n=1417
Exposed to intervention
n=1356Relative Risk
P-value
Number of women offered and accepting membrane sweepingNumber (%) 629 (44.4%) 634 (46.8%)
Cluster adjusted 1.06 (0.97, 1.16) 0.21Time and cluster adjustedFixed effects time 0.88 (0.69, 1.05) 0.11Linear time effect 0.90 (0.73, 1.11) 0.34
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Example 1: Impact of secular trend
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Unadjusted RR = 1.06 95% CI (0.97, 1.16)
Adjusted (for time) RR = 0.88 95% CI (0.69, 1.05)
Rising Tide?
Contamination?
Explanations
• Rising tide– General move towards improving care – perhaps due
to very initiative that prompted study investigators to do this study
• Contamination– Unexposed clusters became exposed before their
randomisation date• Lack of precision
– Intervention wasn’t ruled out as being effective
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Example 2
Example 2: Critical care outreach
• Intervention: Critical care outreach
• Setting: Hospital in Iran
• Clusters: Wards
• Outcome: Mortality
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Example 2: Design
Example 2: Underlying trend
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Example 2: results
Unexposed to intervention
Exposed to intervention
Treatment effect P-value
Number of Patients 7,802 10,880
Mortality Number (%) 370 (4.74) 384 (3.53) OR (95% CI)Unadjusted 0.73 (0.64, 0.85) 0.000Cluster adjusted 1.02 (0.83, 1.26) 0.817Fixed effects for time 0.82 (0.56, 1.19) 0.297Linear effect for time 0.96 (0.76, 1.22) 0.750Covariate adjusted 0.97 (0.64, 1.47) 0.489
Example 2: Underlying trend
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Unadjusted OR = 1.02 95% CI (0.83, 1.26)
Adjusted OR = 0.82 95% CI (0.56,1.19)
Lack of power?
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Explanations
• Rising tide– General move towards improving care – perhaps due
to very initiative that prompted study investigators to do this study
• Contamination– Unexposed clusters became exposed before their
randomisation date• Lack of precision
– Intervention wasn’t ruled out as being effective
Models fitted
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Parameter estimation
• Models fitted used Stata 13 – Used meglm function – Uses mean-variance adaptive Gauss-Hermite quadrature– Default number of integration points (7)– Experienced convergence difficulty (LOS example) then used
the Laplace approximation – but clear instability
• Used random effects– GEE alternative– GEE possibly more robust to model miss-specification – GEE possibly problematic when small number of clusters (there
exist adjustments)
Model assumptions and extensions
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Model assumptions 1
• Underlying secular trend
– The underlying secular trend is same across all clusters
Variation in underlying secular trends
S is strata
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Strata 1
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Strata 3
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Model assumptions 2
• Time invariant treatment effect
– There is no delayed intervention effect
– No change in intensity of the effect over the course of time
– No time by treatment interaction
– Time (since introduction) isn't an effect modifier
Time variant treatment effect
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Control
Intervention
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Model assumptions 3
• Intra cluster correlation
– The correlation between two individuals is independent of time
– Two observations in the same cluster / time period have the same degree of correlation as two observations in the same cluster but different time periods
Time
Model assumptions 4
• Treatment effect heterogeneity
– The effect of the intervention is the same across all clusters
– Typical assumption in CRTs
– In a meta-analysis common to assume between cluster heterogeneity in treatment effect
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Summary
• Time is a potential partial confounder
• Designs which are completely confounded with time shouldn’t be used
• Time must be allowed for as a covariate in primary analysis
• Model extensions require sufficient power and pre-specification
References
• Scott JM, deCamp A, Juraska M, Fay MP, Gilbert PB. Finite-sample corrected generalized estimating equation of population average treatment effects in stepped wedge cluster randomized trials. Stat Methods Med Res. 2014 Sep 29. pii: 0962280214552092. [Epub ahead of print] PubMed PMID: 25267551.
• Ukoumunne OC, Carlin JB, Gulliford MC. A simulation study of odds ratio estimation for binary outcomes from cluster randomized trials. Stat Med. 2007 Aug 15;26(18):3415-28. PubMed PMID: 17154246.
• Heo M, Leon AC. Comparison of statistical methods for analysis of clustered binary observations. Stat Med. 2005 Mar 30;24(6):911-23. PubMed PMID: 15558576
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